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Single-Cell-Based Models in Biology and Medicine

  • Book
  • © 2007

Overview

Editors:
  1. Alexander R. A. Anderson

    1. Division of Mathematics, University of Dundee, Dundee, UK

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  2. Mark A. J. Chaplain

    1. Division of Mathematics, University of Dundee, Dundee, UK

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    You can also search for this editor in PubMed   Google Scholar

  3. Katarzyna A. Rejniak

    1. Division of Mathematics, University of Dundee, Dundee, UK

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  • Focuses on structural, dynamical and functional aspects of cellular systems
  • Presents corresponding experiments and mathematical models
  • Introduces recent model approaches with applications
  • Includes applied issues such as tumor cell growth, blood clotting and biotechnology

Part of the book series: Mathematics and Biosciences in Interaction (MBI)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-ix
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  2. Hybrid Multiscale Models

    1. Front Matter

      Pages 1-1
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    2. A Hybrid Multiscale Model of Solid Tumour Growth and Invasion: Evolution and the Microenvironment

      • Alexander R. A. Anderson
      Pages 3-28

    3. Lattice-gas Cellular Automaton Modeling of Developing Cell Systems

      • Andreas Deutsch
      Pages 29-51

    4. Two-dimensional Multiscale Model of Cell Motion in a Chemotactic Field

      • Mark Alber, Nan Chen, Tilmann Glimm, Pavel Lushnikov
      Pages 53-76

  3. The Cellular Potts Model and Its Variants

    1. Front Matter

      Pages 77-77
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    2. Magnetization to Morphogenesis: A Brief History of the Glazier-Graner-Hogeweg Model

      • James A. Glazier, Ariel Balter, Nikodem J. Popławski
      Pages 79-106

    3. The Cellular Potts Model and Biophysical Properties of Cells, Tissues and Morphogenesis

      • Athanasius F. M. Marée, Verônica A. Grieneisen, Paulien Hogeweg
      Pages 107-136

    4. The Cellular Potts Model in Biomedicine

      • Nicholas J. Savill, Roeland M. H. Merks
      Pages 137-150

    5. The Glazier-Graner-Hogeweg Model: Extensions, Future Directions, and Opportunities for Further Study

      • Ariel Balter, Roeland M. H. Merks, Nikodem J. Popławski, Maciej Swat, James A. Glazier
      Pages 151-167

  5. Viscoelastic Cell Models

    1. Front Matter

      Pages 241-241
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    2. Cell-based Models of Blood Clotting

      • Aaron L. Fogelson
      Pages 243-269

    3. A 3-D Deformable Ellipsoidal Cell Model with Cell Adhesion and Signaling

      • Eirikur Palsson
      Pages 271-299

    4. Modelling the Development of Complex Tissues Using Individual Viscoelastic Cells

      • Katarzyna A. Rejniak
      Pages 301-323

  6. Back Matter

    Pages 325-349
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Keywords

About this book

Many different single-cell-based models have been developed and applied to biological and medical problems. Computational approaches used are Monte-Carlo simulations, energy minimisation techniques, volume conservation laws, solutions of the equations of motion for each individual cell or for each point on the cell membrane. They differ in the level of detail that defines the cell structure and subsequently in the number of individual cells that the model can incorporate.

This volume presents a collection of mathematical and computational single-cell-based models and their application. The main sections cover four general model groupings: hybrid cellular automata, cellular potts, lattice-free cells, and viscoelastic cells. Each section is introduced by a discussion of the applicability of the particular modelling approach and its advantages and disadvantages, which will make the book suitable for students starting research in mathematical biology as well as scientists modelling multicellular processes.

Editors and Affiliations

  • Division of Mathematics, University of Dundee, Dundee, UK

    Alexander R. A. Anderson, Mark A. J. Chaplain, Katarzyna A. Rejniak

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